Abstract
A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a method is proposed for generating all such solutions. It is based on the energy density and the radial pressure as seeding functions. Numerous relations between the realistic conditions are found and the need for a graphic proof is reduced just to one pair of inequalities. This general formalism is illustrated with an example of a class of solutions with linear equation of state and simple energy density. It is found that the solutions depend on three free constants and concrete examples are given. Some other popular models are studied with the same method.
Highlights
The study of relativistic stellar structure is more than 100 years old
Numerous relations between the realistic conditions are found and the need for a graphic proof is reduced just to one pair of inequalities. This general formalism is illustrated with an example of a class of solutions with linear equation of state and simple energy density
Even with one free parameter the graphics become 3D. This method is rather close to numerical simulations and not to an analytical study. Is it possible to reduce the number of graphic proofs? Do any relations exist between the numerous conditions, concerning just a few basic characteristics of the model, so that some of the conditions follow from the others in the general case? These questions will be dealt with
Summary
The study of relativistic stellar structure is more than 100 years old. It began with the discovery in 1916 by Karl Schwarzschild of a universal vacuum exterior solution [1]. For a long time the star interior was considered to be made of a perfect fluid, which has equal radial ( pr ) and tangential ( pt ) pressures This leads to the isotropic condition pr = pt , imposed on the Einstein equations. But the regularity conditions were not studied For isotropic solutions it becomes the algorithm of Lake [20]. Its anisotropic version was used by Bowers and Liang [5] to find the first well-known star model, which has constant ρ, while Δ is given in a form suitable to solve the TOV equation. 6 an example is given—solutions with linear EOS and simple energy density In this method the main object we study is the tangential pressure, which is done in Sect.
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